$\dfrac{ 5j - 5k }{ -10 } = \dfrac{ 10j - 3l }{ -7 }$ Solve for $j$.
Answer: Multiply both sides by the left denominator. $\dfrac{ 5j - 5k }{ -{10} } = \dfrac{ 10j - 3l }{ -7 }$ $-{10} \cdot \dfrac{ 5j - 5k }{ -{10} } = -{10} \cdot \dfrac{ 10j - 3l }{ -7 }$ $5j - 5k = -{10} \cdot \dfrac { 10j - 3l }{ -7 }$ Multiply both sides by the right denominator. $5j - 5k = -10 \cdot \dfrac{ 10j - 3l }{ -{7} }$ $-{7} \cdot \left( 5j - 5k \right) = -{7} \cdot -10 \cdot \dfrac{ 10j - 3l }{ -{7} }$ $-{7} \cdot \left( 5j - 5k \right) = -10 \cdot \left( 10j - 3l \right)$ Distribute both sides $-{7} \cdot \left( 5j - 5k \right) = -{10} \cdot \left( 10j - 3l \right)$ $-{35}j + {35}k = -{100}j + {30}l$ Combine $j$ terms on the left. $-{35j} + 35k = -{100j} + 30l$ ${65j} + 35k = 30l$ Move the $k$ term to the right. $65j + {35k} = 30l$ $65j = 30l - {35k}$ Isolate $j$ by dividing both sides by its coefficient. ${65}j = 30l - 35k$ $j = \dfrac{ 30l - 35k }{ {65} }$ All of these terms are divisible by $5$ $j = \dfrac{ {6}l - {7}k }{ {13} }$